System and method for generating a tomographic reconstruction filter

ABSTRACT

A system for generating a reconstruction filter for an imaging scanner comprises a model bank that includes a model for generating the reconstruction filter, a filter criteria bank that includes filter criteria for generating the reconstruction filter, and a filter generator that generates the reconstruction filter based on the filter model and the filter criteria. In one non-limiting instance, the model is based on minimizing a cost function that includes predetermined filter criteria such as image contrast. In another non-limiting instance, the cost function includes terms relating to spatial resolution, noise and a signal visual perception in the presence of noise.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional application Ser.No. 61/176,230 filed May 7, 2009, which is incorporated herein byreference.

The following generally relates to a reconstruction filter, and findsparticular application to computed tomography (CT). However, it alsoamenable to other medical imaging applications and to non-medicalimaging applications.

A computed tomography (CT) scanner generally includes an x-ray tubemounted on a rotatable gantry that rotates around an examination regionabout a longitudinal or z-axis and emits radiation. A detector arraysubtends an angular arc opposite the examination region from the x-raytube. The detector array detects radiation that traverses theexamination region (and a subject or object therein), and generatesprojection data indicative thereof. A reconstructor reconstructs theprojection data based on a reconstruction algorithm such as a filteredback-projection reconstruction algorithm and generates volumetric imagedata indicative of the scanned subject or object. The volumetric imagedata can be processed to generate one or more images indicative of thescanned subject or object.

Conventional filtered back-projection reconstruction algorithms of conebeam CT have been based on a two dimensional (2D) image Fourierdecomposition of the data followed by a Fourier composition. In general,a CT image of gray levels can be regarded as a 2D function of the X-rayattenuation coefficient within a slice of the subject or object.According to the Fourier theorem, this function can be decomposed intowaves (Fourier components) that propagate in the transverse plane. Assuch, this function can be written as a linear combination or asuperposition of waves. The waves are parameterized in the Fourierdomain by the absolute value of their frequency k and by their directiongiven by the polar angle θ. During reconstruction, the amplitudes andthe phases of the waves are estimated using processing steps based onthe Radon slice theorem. The waves are then summed up to form the image.

The wave amplitudes estimated during the reconstruction areintentionally modified before the summation of the waves. Thismodification is controlled by the reconstruction filter. By way ofexample, due to the finite width of the X-ray beam, the amplitudes ofthe high-frequency waves estimated from the measurement are smaller thantheir real values within the X-ray attenuation correction map. Knowingin advance the frequency dependent ratio between the estimated valuesand the true values of the amplitudes (the modulation transfer function(MTF) of the system), the estimated amplitudes of the high-frequencywaves can be emphasized to compensate for the drop of the MTF at thesefrequencies. However, de-emphasizing the values of the estimatedamplitudes enables reducing the noise power spectrum (NPS) in thereconstructed image. The main origin for this noise is the Poissonprobability distribution of the photons to reach the detectors.

Tailoring reconstruction filters for a particular scanner generallyincludes emphasizing and de-emphasizing certain frequency contents.Conventionally, optimizing a particular filter for a particularapplication has been performed based on user (e.g., radiologists,application specialist, etc.) feedback. Unfortunately, optimizingreconstruction filters empirically based on user feedback can extend theoptimization process over a relatively long period of time. Furthermore,such optimization generally is limited to tuning the filter frequencydependence to a small group of functions spanned by a few pre-definedparameters.

Aspects of the present application address the above-referenced mattersand others.

According to one aspect, a system for generating a reconstruction filterfor an imaging scanner comprises a model bank that includes a model forgenerating the reconstruction filter, a filter criteria bank thatincludes filter criteria for generating the reconstruction filter, and afilter generator that generates the reconstruction filter based on thefilter model and the filter criteria.

In another embodiment, a method includes minimizing a cost functionrepresented as a sum of two terms, wherein a first term penalizes a lossof a spatial resolution attributed to an imaging system and a secondterm penalizes a loss of signal detection due to image noise.

In another embodiment, a computer readable storage medium containinginstructions which, when executed by a computer, cause the computer toperform the acts of minimizing a cost function represented as a sum of afirst term that penalizes a loss of a spatial resolution attributed toan imaging system and a second term that penalizes a loss of signaldetection due to image noise.

In another embodiment, a method includes generating a filter byminimizing a cost function based on predetermined contrast criteriaincluding terms relating to the loss of spatial resolution and termsrelating to a loss of the visual signal perception in the presence ofnoise.

The invention may take form in various components and arrangements ofcomponents, and in various steps and arrangements of steps. The drawingsare only for purposes of illustrating the preferred embodiments and arenot to be construed as limiting the invention.

FIG. 1 illustrates an example imaging system.

FIG. 2 illustrates an example method.

FIG. 1 illustrates an imaging system or CT scanner 100. The imagingsystem 100 includes a stationary gantry 102 and a rotating gantry 104,which is rotatably supported by the stationary gantry 102 and rotatesaround an examination region 106 about a rotating frame rotation centeralong a longitudinal or z-axis. A radiation source 108, such as an x-raytube, is supported by the rotating gantry 104. The radiation source 108emits radiation. A source collimator collimates the emitted radiation toform a generally cone, fan, wedge, or otherwise shaped beam thattraverses the examination region 106. A radiation sensitive detectorarray 110 subtends an angular arc opposite the radiation sources 108across the examination region 106 and detects radiation traversing theexamination region 106. The detector array 110 generates projection dataor a signal indicative of the detected radiation. A patient support,such as a couch, supports an object or subject in the examination region106.

A reconstructor 112 reconstructs the signal from the detector array 110based on a selected reconstruction algorithm and generates volumetricimage data indicative thereof. A general-purpose computing system servesas an operator console 114. Software resident on the console 114 allowsthe operator to control the operation of the system 100 by selecting thescanning protocol, accepting or changing the reconstruction filter forthe selected protocol, etc. A filter identifier 116 identifies theselected filter in a filter bank 118, which may include a plurality ofdifferent filters (e.g., sharp, smooth, etc.) variously tuned fordifferent applications.

A reconstruction filter generator 120 generates one or morereconstruction filters (e.g., sharp, smooth, etc.) that can be used bythe reconstructor 112. The filter generator 120 can be part of thesystem 100 or remote from the system 100 such as part of a separatecomputer, workstation, or the like. The filter generator 120 cangenerate a reconstruction filter based on various pre-determinedcriteria stored in a filter criteria bank 122, a filter model stored ina filter model bank 124, and/or other information. By way ofnon-limiting example, in one instance the filter generator 120 generatesa reconstruction filter (without user interaction such as without tuningof any parameters) based on predetermined image contrast criteria and acost function. In other embodiments, the filter is otherwise generated.

The cost function can be represented in the Fourier domain as a sum oftwo integrals over k expressed in terms of the MTF and NPS of thesystem. The MTF and NPS depend on scanner geometry such as detectorpixel size and the x-ray tube-to-detector distance and can be measured,simulated or approximated, without emphasizing or de-emphasizing theestimated wave amplitudes. This can be done by choosing thereconstruction filter values to be one for all frequencies that arelower than the frequency v_(c) defined, as an example, as the cut-offfrequency of the MTF. Generally, the first integral of the cost functioncorresponds to the loss of signal detection ability due to spatialsmearing, and the second integral of the cost function corresponds tothe loss of the ability to detect the signal due to image noise. The twointegrals can contain similar or different integrants and may take intoaccount a priori information.

As described in greater detail next, in one non-limiting instance thefilter is generated by minimizing a cost function. For this example, thecost function is represented in terms of a signal power spectrum (SPS),which represents the statistical energy distribution of the signal inthe Fourier domain. In CT, the SPS can be defined based on an ensembleof attenuation correction maps, and the dependence of the SPS on thewave frequency can be represented as shown in EQUATION 1:SPS=SPS(k,r),  EQUATION 1:where k represents an absolute value of the frequency and r represents adistance between an image pixel and the rotating frame rotation center.Assuming the dependence on r is not significant, the SPS can berepresented as shown in EQUATION 2:

$\begin{matrix}{{{S\; P\;{S(k)}} \propto \left( \frac{k_{0}}{k} \right)^{p}},{\left. p \right.\sim 1.9},} & {{EQUATION}\mspace{14mu} 2}\end{matrix}$With the illustrated embodiment, the reconstruction filters slightlyvary for p in a range of one (1) to one and nine tenths (1.9).

The loss of resolution in the cost function can be penalized byconsidering the power spectrum of an error image taken as the differencebetween an image obtained for a given reconstruction filter F(k),excluding noise and aliasing artifact, and an image that represents theradiation attenuation coefficient map. Based on the above, the integrantof the first integral of the cost function can be represented as aquadratic relationship between the amplitudes and the power spectrum asshown in EQUATION 3:INT_(s)(k)∝SPS(k)·(1−MTF(k)·F(k))².  EQUATION 3:

In this example, the second integral of the cost function takes intoaccount the function I(k′/k), where k′ and k respectively represent thefrequency absolute values of a signal wave and of a noise wave. Thefunction I(k′/k) describes how the frequency ratio k′/k influences theability of a human observer to detect the signal in the presence of thenoise component.

Various definitions can be used to for I(k′/k). The following describesa suitable example. Consider a signal image composed of only onesinusoid such as a plane wave with a frequency absolute value of k′oscillating within the image around zero. Consider also a noise imageformed by creating a white noise image (with no correlation between thevalues of neighbor pixels) using a random Gaussian generator centered atzero. A 2D Fourier de-composition can be performed on the white noiseimage, and the amplitudes can be set to zero for all waves except thosehaving frequencies with an absolute value that falls between k−δ andk+δ. A Fourier composition can then be performed on the de-composedsignal.

Note that the noise image obtained by the above steps contains waves ofdifferent directions (θ). In other words, these waves occupy a ring inthe frequency domain bounded by the radii k−δ and k+δ. The variance ofthe noise image and of the signal image described above can be expressedas shown in EQUATION 4:

$\begin{matrix}{\sigma = {\lim\limits_{N->\infty}\frac{\sum\limits_{s = 1}^{N}\left( {{i(s)} - {\sum\limits_{q = 1}^{N}{{i(q)}/N}}} \right)^{2}}{N - 1}}} & {{EQUATION}\mspace{14mu} 4}\end{matrix}$where N is a number of image pixels and i(s)\i(q) is a value of theimage in pixel s\q. The signal image variance can be increased so that ahuman observer would detect the signal when the noise image is added tothe signal image. Alternatively, the signal image variance can bedecreased so that the human observer would not detect any more signalafter the noise image is added to the signal image.

Consider therefore the minimal ratio between the signal image varianceand the noise image variance in which the observer still detects thesignal. Allowing the observer to zoom in and out of the image, thisminimal variance ratio depends only on the ratio between k′ and k. Inone embodiment, I(k′/k) is considered as this minimal ratio. In oneinstance, I(k′/k) can be empirically estimated. The empirical measuredpoints can be fit later to a Gaussian dependence of I on log(k′/k).

The following discusses how to include in the cost function the amountby which the informative signal is degraded due to the noise waves lyingwithin a ring shaped region of frequencies having absolute valuescentered at k. This amount is proportional to the product of NPS(k) bythe square of the reconstruction filter at that k denoted by F(k). Assuch, the integrant of the second integral generally follows EQUATION 5:INT_(noise)(k)∝NPS(k)·F(k)²,  EQUATION 5:where NPS(k) represents the noise power spectrum at k obtained for usingF(k)=1 for all frequencies lower than v_(c). As such, EQUATION 5 can beused to determine the noise power density at k.

The integrant of the second integral can also be proportional to theeffectiveness in which this power density can degrade the detection ofthe signal distributed by SPS (k). In one embodiment, this effectivenesscan be estimated as the integral of I(k′/k) over the signal frequency k′weighted according to the value of the signal power spectrum at thisfrequency as shown in EQUATION 6:

$\begin{matrix}{{{e_{n}(k)} = {\int_{0}^{v_{c}}{{\mathbb{d}k^{\prime}}{k^{\prime} \cdot S}\; P\;{{S\left( k^{\prime} \right)} \cdot {I\left( {k^{\prime},k} \right)}}}}},} & {{EQUATION}\mspace{14mu} 6}\end{matrix}$where k′ is the Jacobian determinant of the transformation matrix fromCartesian to polar coordinates. As noted above, SPS (k′) represents anensemble of attenuation coefficient maps. In one instance, the ensemblecan be translated to an ensemble of reconstructed CT images, forexample, by multiplying the integrant in EQUATION 6 by MTF (k′)²·F(k′)².

From EQUATIONS 5 and 6, the integrant of the cost function includesproducts of F(k)²·F(k′)². However, in another embodiment as anapproximation F(k′)² in EQUATION 6 is replaced by one, which cansimplify the solution for the filter F(k) and provide a global minimumfor the cost function. e_(n)(k) in EQUATION 6 can also be expressed as adimensionless function in terms of a weighted average of I(k′/k) asshown in EQUATION 7:

$\begin{matrix}{{{e_{n}^{A}(k)} = \frac{\int_{0}^{v_{s}}{{\mathbb{d}k^{\prime}}{k^{\prime} \cdot S}\; P\;{{S\left( k^{\prime} \right)} \cdot M}\; T\;{{F\left( k^{\prime} \right)}^{2} \cdot {I\left( {k^{\prime},k} \right)}}}}{\int_{0}^{v_{c}}{{\mathbb{d}k^{\prime}}{k^{\prime} \cdot S}\; P\;{{S\left( k^{\prime} \right)} \cdot M}\; T\;{F\left( k^{\prime} \right)}^{2}}}},} & {{EQUATION}\mspace{14mu} 7}\end{matrix}$where A represents either an approximation or an average over k′.

From EQUATIONS 1, 3, 5 and 7, the cost function can be represented asshown in EQUATION 8:

$\begin{matrix}{{{E_{\alpha}\left( {F(k)} \right)} = {{\int_{0}^{v_{c}}{{{\mathbb{d}{kk}} \cdot S}\; P\;{{S(k)} \cdot \left( {1 - {M\; T\;{{F(k)} \cdot {F(k)}}}} \right)^{2}}}} + {\alpha \cdot {\int_{0}^{v_{c}}{{{\mathbb{d}{kk}} \cdot N}\; P\;{{S(k)} \cdot {e_{n}^{A}(k)} \cdot {F(k)}^{2}}}}}}},} & {{EQUATION}\mspace{14mu} 8}\end{matrix}$where E_(α)(F(k)) represents a functional, or scalar, value that dependson the reconstruction filter F(k). The parameter α that multiplies thesecond term of the cost function is used to balance between the signaldegradation caused by the loss of spatial resolution and that caused bynoise. In one embodiment, this parameter is calculated automaticallytogether with the reconstruction filter F(k) as described next.

The image noise variance at the point (x, y) can be represented as shownin EQUATION 9:

$\begin{matrix}{{{\sigma\left( {x,y} \right)} = {\left( \frac{\pi}{M_{proj}} \right)^{2} \cdot 2 \cdot \tau \cdot \left( {\sum\limits_{i = 1}^{M_{proj}}\frac{1}{\overset{\_}{N}\left( {x,y,{\theta(i)}} \right)}} \right) \cdot {\int_{0}^{v_{c}}{{\mathbb{d}{kk}^{2}}{F(k)}^{2}}}}},} & {{EQUATION}\mspace{14mu} 9}\end{matrix}$

where M_(proj) represents a number of projections back-projected to thepixel, τ represents the radial increment between the readings, and N(x,y, θ(i)) represents a mean value of the number of photons that reach thedetector belonging to the reading of the projection angled along θ thatis intersecting the point (x, y).

The ratio between the image noise variance obtained using thereconstruction filter F(k) and the image noise variance obtained byreplacing all its values by one (1) can be represented as shown inEQUATION 10:

$\begin{matrix}\begin{matrix}{{{rv}\left( {F(k)} \right)} \equiv {{\sigma\left( {F(k)} \right)}/{\sigma\left( {F(k)}\Rightarrow 1 \right)}}} \\{= {\frac{\int_{0}^{v_{c}}{{\mathbb{d}{kk}^{2}}{F(k)}^{2}}}{\int_{0}^{v_{c}}{\mathbb{d}{kk}^{2}}}.}}\end{matrix} & {{EQUATION}\mspace{14mu} 10}\end{matrix}$Due to different effects like fan-to-parallel re-binning of theprojections, cross-talk between the detector pixels and others, thedependence of ry on F(k) may differ from the approximation in EQUATION10. However, it can still be calculated based on the measured orsimulated NPS(k) as shown in EQUATION 11:

$\begin{matrix}{{{rv}\left( {F(k)} \right)} = \frac{\int_{0}^{v_{c}}{{\mathbb{d}{kk}}\; N\; P\;{S(k)}{F(k)}^{2}}}{\int_{0}^{v_{c}}{{\mathbb{d}{kk}}{N\; P\;{S(k)}}}}} & {{EQUATION}\mspace{14mu} 11}\end{matrix}$In one instance, for a given value of rv(F(k)) denoted by rv_(g), theparameter α and the filter F(k) are calculated together automatically bythe following fast converging iterative procedure. By way of example, αis set to α₀=1, and F₀(k) is calculated as the filter that minimizes thecost function E_(α) ₀ (F(k)). This can be expressed as shown in EQUATION12:

$\begin{matrix}{{F_{0}(k)} = {\min\limits_{\{{F{(k)}}\}}{{E_{\alpha_{0}}\left( {F(k)} \right)}.}}} & {{EQUATION}\mspace{14mu} 12}\end{matrix}$n iterations are performed as shown in EQUATION 13:

$\begin{matrix}\begin{matrix}{\alpha_{1} = \frac{\alpha_{0} \cdot {{rv}\left( {F_{0}(k)} \right)}}{{rv}_{g}}} & {{F_{1}\left( {{rv}_{g},k} \right)} = {\min\limits_{\{{F{(k)}}\}}{E_{\alpha_{1}}\left( {F(k)} \right)}}} \\{\alpha_{2} = \frac{\alpha_{1} \cdot {{rv}\left( {F_{1}(k)} \right)}}{{rv}_{g}}} & {{F_{2}\left( {{rv}_{g},k} \right)} = {\min\limits_{\{{F{(k)}}\}}{{E_{\alpha_{2}}\left( {F(k)} \right)}\mspace{14mu}\ldots}}} \\\ldots & \; \\{\alpha_{n} = \frac{\alpha_{n - 1} \cdot {{rv}\left( {F_{n - 1}(k)} \right)}}{{rv}_{g}}} & {{F_{n}\left( {{rv}_{g},k} \right)} = {\min\limits_{\{{F{(k)}}\}}E_{{\alpha_{n}{({F{(k)}})}},}}}\end{matrix} & {{EQUATION}\mspace{14mu} 13}\end{matrix}$with stopping criterion set for F_(n)(rv_(g),k) as shown in EQUATION 14.

$\begin{matrix}{{{{abs}\left( {\frac{{rv}\left( {F_{n}\left( {{rv}_{g},k} \right)} \right)}{{rv}_{g}} - 1} \right)} \leq ɛ},} & {{EQUATION}\mspace{14mu} 14}\end{matrix}$where a typical value for ε is about 10⁻⁴, and the reconstruction filtercan be expressed as shown in EQUATION 15:F(rv _(g) ,k)=F _(n)(rv _(g) ,k).  EQUATION 15

Present commercial CT scanners contain a group of reconstruction filtersthat offer a set of different values for rv(F(k)). For embodimentsherein, the values for rv_(g) can optionally be set according to thisset. Changing the scanner geometry by reducing, for example, the pixelsize can motivate the inclusion of new values for rv_(g), higher in thiscase. In any case, even when the value of rv_(g) taken for the newfilter equals to that of the old filter, the frequencies are emphasizedor de-emphasized differently by the old filter and by the new optimalfilter obtained by EQUATIONS 8 and 12-14.

Based on EQUATION 7, a reconstruction filter that minimizes the costfunction in EQUATION 8 can be represented as show in EQUATION 16:

$\begin{matrix}{{F_{i}(k)} = {\frac{M\; T\;{F(k)}}{{M\; T\;{F(k)}^{2}} + {{\alpha_{i} \cdot \left( {k/k_{0}} \right)^{p} \cdot N}\; P\;{{S(k)} \cdot {e_{n}^{A}(k)}}}}.}} & {{EQUATION}\mspace{14mu} 16}\end{matrix}$In instance where NPS(k˜0)=0 and MTF(k˜0)=1, EQUATION 16 renders a zeroderivative of F_(i)(k) at k=0. Due to the finite width of the beams, theMTF(k) often drops down before NPS(k). Based on EQUATION 16, within theregion where α_(i)·(k/k₀)^(p)·NPS(k)·e_(n) ^(A)(k)>>MTF(k), F(k) mayrapidly drop.

FIG. 2 illustrates a method for automatically generating areconstruction filter for an imaging system. At 202, predeterminedfilter criteria is identified. For this example, the criteria is imagecontrast, including the ability of a human observer to detect the signalin the presence of noise, and the filter is generated to optimize thepredetermined image contrast criteria. In other embodiments, the filtercan be generated based on other criteria. At 204, imagingcharacteristics of the system such as an MTF, an NPS, an SPS and/orother characteristic of the system are identified. As noted above, theMTF and the NPS can be measured, simulated or approximated. At 206, acost function represented in terms of the imaging characteristics isidentified. At 208, a filter is generated by minimizing the costfunction based on the predetermined filter criteria, the MTF, and theNPS. As described herein, the cost function can be represented in theFourier domain over the frequencies (k) of the waves. Such a costfunction can take into account the loss of signal detection ability dueto spatial smearing and the loss of the ability to detect the signal dueto image noise. At 210, the filter is employed to reconstruct projectiondata generated by an imaging system. At 212, the above can be repeatedfor one or more filters and/or one or more similar or different imaginessystems.

The above can be implemented as a console application of a scannerand/or an image processing or planning workstation. By way of example,the above may be implemented by way of computer readable instructions,which when executed by a computer processor(s) (a processor of theconsole or workstation), cause the processor(s) to carry out thedescribed acts. In such a case, the instructions are stored in acomputer readable storage medium associated with or otherwise accessibleto the relevant computer.

The invention has been described herein with reference to the variousembodiments. Modifications and alterations may occur to others uponreading the description herein. It is intended that the invention beconstrued as including all such modifications and alterations insofar asthey come within the scope of the appended claims or the equivalentsthereof.

What is claimed is:
 1. A system for generating a reconstruction filterfor an imaging scanner, comprising: a model bank memory that includes afilter model for generating the reconstruction filter, wherein thefilter model includes a cost function including a sum of two terms,including a first term that penalizes a loss of a spatial resolutionattributed to the imaging scanner and a second term that penalizes aloss of signal detection due to image noise, wherein the second term isa function of a predetermined signal-to-noise ratio that corresponds toan approximation of a minimal signal-to-noise variance ratio at which ahuman observer is able to discern a known signal from noise; a filtercriteria bank memory that includes filter criteria for generating thereconstruction filter; and a filter generator, executed by amicroprocessor, that generates the reconstruction filter based on thefilter model and the filter criteria.
 2. The system of claim 1, whereinthe cost function includes only the two terms.
 3. The system of claim 1,wherein the cost function models degradation of the filter criteria. 4.The system of claim 2, wherein the filter generator generates the filterby minimizing the cost function.
 5. The system of claim 1, wherein thefilter criteria includes optimizing image contrast.
 6. The system ofclaim 1, wherein the reconstruction filter is represented as:$\frac{{MTF}(k)}{{{MTF}(k)}^{2} + {\alpha_{i} \cdot \left( {k/k_{0}} \right)^{p} \cdot {{NPS}(k)} \cdot {e_{n}^{A}(k)}}},$where MTF is a modulation transfer function,α_(i)·(k/k₀)^(P)·NPS(k)·e_(n) ^(A)(k)>>MTF(k), k represents an absolutevalue of a frequency, α represents a parameter, NPS represents a noisepower spectrum, e represents an estimated effectiveness in which a powerdensity degrade the detection of a signal distributed by a signal powerspectrum, i, 0, and n are subscripts, p is a power, and A represents anapproximation or an average.
 7. The system of claim 6, wherein the firstand second terms depend on a modulation transfer function of thescanner, a noise power spectrum of the scanner, and a statisticallyaveraged signal power spectrum of the scanned subject or object.
 8. Thesystem of claim 1, wherein the cost function is represented in terms ofa signal power spectrum.
 9. The system of claim 1, wherein the loss ofresolution in the cost function is penalized based on a power spectrumof an error image taken as a difference between an image obtained for agiven reconstruction filter, excluding noise and aliasing artifact, andan image that represents a radiation attenuation coefficient map. 10.The system of claim 1, wherein the signal-to-noise variance ratio is aratio between a variance of a single sinusoid signal at particularfrequency and between a variance of an isotropic noise image containinga noise power spectrum that is finite only on a ring of a finite widthin a Fourier domain.
 11. The system of claim 10, wherein the minimalsignal-to-noise variance ratio is measured empirically and smoothedusing a Gaussian fit.
 12. The system of claim 6, wherein the filtergenerator minimizes the cost function through a balancing parameter thatbalances the first and second terms.
 13. The system of claim 12, whereinthe balancing parameter is determined through at least one predefinedparameter.
 14. The system of claim 13, wherein the predefined parameteris a ratio between an image noise variance corresponding to an optimizedfilter and an image noise variance corresponding to a predeterminedreference filter.
 15. The system of claim 14, wherein the predeterminedreference filter has values equal to one and rapidly decreases at apredefined frequency.
 16. The system of claim 14, further includingdetermining the balancing parameter and the optimized filtersimultaneously based on an automatic converging iterative approach. 17.The system of claim 1, wherein the system includes a computer tomographyscanner.
 18. A non-transitory computer readable storage mediumcontaining instructions which, when executed by a computer, cause thecomputer to perform an act of: generating a reconstruction filter byminimizing a cost function including only two terms represented as a sumof a first term that penalizes a loss of a spatial resolution attributedto an imaging system and a second term that penalizes a loss of signaldetection due to image noise, wherein the second term is based on apredetermined approximation of a minimal signal-to-noise variance ratioat which a human observer is able to discern a known signal from noise.19. The computer readable storage medium of claim 18, wherein the firstand the second terms are functions of a modulation transfer function ofthe imaging system and of a noise power spectrum of the imaging system.20. The computer readable storage medium of claim 18, wherein the costfunction is minimized based on a balancing parameter that balances thefirst and second terms.
 21. The computer readable storage medium ofclaim 20, wherein the balancing parameter is determined according to apredefined ratio between an image noise variance corresponding to anoptimized filter and the image noise variance corresponding to apredefined reference filter.
 22. A method for generating areconstruction filter for an imaging scanner, comprising: obtaining frommodel memory a filter model that includes a cost function including asum of two terms, including a first term that penalizes a loss of aspatial resolution attributed to the imaging scanner and a second termthat penalizes a loss of signal detection due to image noise, whereinthe second term is a function of a predetermined signal-to-noise ratiothat corresponds to an approximation of a minimal signal-to-noisevariance ratio at which a human observer is able to discern a knownsignal from noise; obtaining from filter criteria memory filter criteriafor generating the reconstruction filter; and with a microprocessor, thereconstruction filter based on the filter model and the filter.